A Few Thoughts About Quarks

Authors: Richard KERNER

Abstract: We present a novel approach to the description of quark fields, based on the use of Z_{3}-graded algebras. After introducing Z_{3}-graded generalizations of Grassmann and Clifford algebras, we discuss the cubic version of Dirac's equation for the quarks, which after diagonalization leads to the third-order partial differential equation for the wave functions. We show how certain cubic and quadratic products of these functions can be interpreted as solutions of first-and second-order differential equations.